Problem: What is the value of the following logarithm? $\log_{625} 5$
If $b^y = x$ , then $\log_{b} x = y$ Notice that $5$ is the fourth root of $625$ That is, $\sqrt[4]{625} = 625^{1/4} = 5$ Thus, $\log_{625} 5 = \dfrac{1}{4}$.